Question

determine whether the function is periodic?

Answer 1

What is the function??

Answer 2

A function is Periodic if its value changes after a certain interval of time..

For f(t) to be Periodic:

\[f(t) = f(t + T)\] where, \(T\) is the Time Period after which f(t) repeats itself.. :)

Answer 3

Acos(3pi/7 m + pi/8)

Answer 4

Okay..

\[A \cos(\frac{3 \pi}{7}m + \frac{\pi}{8})\]

Answer 5

See, to find the time period or whether the function is periodic, forget the shift given to you, the function is shifted by pi/8, so it will not affect Periodicity.. :)

Answer 6

yes, i know its period.. but m just getting confuse in determining whether the signal is periodic or not.. which is the first step

Answer 7

Now:

To find if it is Periodic or not, the value of its Time Period should be rational.. :)

Answer 8

If Time Period of this function comes out to be a Rational value or number, then your function is Periodic otherwise not..

Answer 9

What is its Period?? You know that??

Answer 10

its 14/3..
but the question given is.. first check whether its periodic or not then find the period..

Answer 11

This is always Periodic..

A cos function is always periodic with period of \(2 \pi\)..

Answer 12

i know.. but the question is.. what z the method of checking whether the function is periodic or not???

Answer 13

Yeah, this is a serious question.. :P

Answer 14

I said check its time period if it is coming to be rational then it is periodic, don't you get this??

Answer 15

Wait, let me do this for you..

Answer 16

\[A \cos(\frac{3 \pi}{7}m + \frac{\pi}{8})\]

Answer 17

Here, frequency is :

\[\omega = \frac{3 \pi}{7}\]

Answer 18

Now,

\(T = \frac{2 \pi}{\omega} = \frac{14}{3}\)

Answer 19

Is this T a rational value?? :)

Answer 20

have got it... n know its periodic

Answer 21

As T is coming out to be rational so, you will say that the function is periodic, with Time period you have just calculated.. :)

Answer 22

Getting or not??